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Williams primes of the form (b-1)•bn+1, least n-values
Description
Here are shown the least n-value ≥ 1 for any base b with 2 ≥ b ≥ 1024 which generates a Williams prime of the form (b-1)•bn+1.
History
- 2019-05-23: Found n = 1822 (b=545), Karsten Bonath
- 2019-05-22: Found n = 9762 (b=536), Karsten Bonath
- 2019-05-22: Found n = 4012 (b=497), Karsten Bonath
- 2019-05-13: Found n = 142876 (b=363), Karsten Bonath
Wanted values
Given here bases and known searched range:
- Searched by Conjectures 'R Us
- 123 [250000]
- 342 [100000]
- 438 [100000]
- 487 [100000]
- 757 [100000]
- 997 [100000]
- 1005 [100000]
- Others
Data
The data file can be found here.
Base | n-value |
---|---|
2 | 1 |
3 | 1 |
4 | 1 |
5 | 2 |
6 | 1 |
7 | 1 |
8 | 2 |
9 | 1 |
10 | 3 |
11 | 10 |
12 | 3 |
13 | 1 |
14 | 2 |
15 | 1 |
16 | 1 |
17 | 4 |
18 | 1 |
19 | 29 |
20 | 14 |
21 | 1 |
22 | 1 |
23 | 14 |
24 | 2 |
25 | 1 |
26 | 2 |
27 | 4 |
28 | 1 |
29 | 2 |
30 | 4 |
31 | 5 |
32 | 12 |
33 | 2 |
34 | 1 |
35 | 2 |
36 | 2 |
37 | 9 |
38 | 16 |
39 | 1 |
40 | 2 |
41 | 80 |
42 | 1 |
43 | 2 |
44 | 4 |
45 | 2 |
46 | 3 |
47 | 16 |
48 | 2 |
49 | 2 |
50 | 2 |
51 | 1 |
52 | 15 |
53 | 960 |
54 | 15 |
55 | 1 |
56 | 4 |
57 | 3 |
58 | 1 |
59 | 14 |
60 | 1 |
61 | 6 |
62 | 20 |
63 | 1 |
64 | 3 |
65 | 946 |
66 | 6 |
67 | 1 |
68 | 18 |
69 | 10 |
70 | 1 |
71 | 4 |
72 | 1 |
73 | 5 |
74 | 42 |
75 | 4 |
76 | 1 |
77 | 828 |
78 | 1 |
79 | 1 |
80 | 2 |
81 | 1 |
82 | 12 |
83 | 2 |
84 | 6 |
85 | 4 |
86 | 30 |
87 | 3 |
88 | 3022 |
89 | 2 |
90 | 1 |
91 | 1 |
92 | 8 |
93 | 2 |
94 | 4 |
95 | 4 |
96 | 2 |
97 | 11 |
98 | 8 |
99 | 2 |
100 | 1 |
101 | 2 |
102 | 1 |
103 | 56 |
104 | 2 |
105 | 12 |
106 | 1 |
107 | 4 |
108 | 5 |
109 | 15 |
110 | 2 |
111 | 1 |
112 | 1 |
113 | 4 |
114 | 3 |
115 | 2 |
116 | 16 |
117 | 3 |
118 | 1 |
119 | 46 |
120 | 1 |
121 | 2 |
122 | 6216 |
123 | 865890 |
124 | 2 |
125 | 16 |
126 | 4 |
127 | 165 |
128 | 72 |
129 | 5 |
130 | 64 |
131 | 14 |
132 | 1 |
133 | 2 |
134 | 50 |
135 | 2 |
136 | 279 |
137 | 12 |
138 | 2 |
139 | 1 |
140 | 2 |
141 | 6 |
142 | 1 |
143 | 4 |
144 | 1 |
145 | 3 |
146 | 4 |
147 | 4 |
148 | 1 |
149 | 2 |
150 | 14 |
151 | 1 |
152 | 8 |
153 | 4 |
154 | 1 |
155 | 6 |
156 | 1 |
157 | 29 |
158 | 1620 |
159 | 16 |
160 | 5 |
161 | 2 |
162 | 1 |
163 | 1 |
164 | 20 |
165 | 1 |
166 | 5 |
167 | 24 |
168 | 1 |
169 | 1 |
170 | 2 |
171 | 52 |
172 | 99 |
173 | 2 |
174 | 1 |
175 | 15 |
176 | 4 |
177 | 1 |
178 | 8 |
179 | 46 |
180 | 2484 |
181 | 2 |
182 | 396 |
183 | 22 |
184 | 3 |
185 | 208 |
186 | 3 |
187 | 8 |
188 | 10 |
189 | 1 |
190 | 1 |
191 | 2 |
192 | 15 |
193 | 1 |
194 | 2 |
195 | 1 |
196 | 60 |
197 | 520 |
198 | 4 |
199 | 8 |
200 | 60 |
201 | 2 |
202 | 46773 |
203 | 2 |
204 | 1 |
205 | 2 |
206 | 2 |
207 | 1 |
208 | 9 |
209 | 2 |
210 | 1 |
211 | 2 |
212 | 4 |
213 | 4 |
214 | 118 |
215 | 2 |
216 | 1 |
217 | 5 |
218 | 44 |
219 | 1 |
220 | 5 |
221 | 24 |
222 | 3 |
223 | 14 |
224 | 2 |
225 | 5 |
226 | 2 |
227 | 16 |
228 | 24 |
229 | 41 |
230 | 2 |
231 | 4 |
232 | 1 |
233 | 16 |
234 | 10 |
235 | 15 |
236 | 4 |
237 | 1 |
238 | 40 |
239 | 50 |
240 | 3 |
241 | 38 |
242 | 4 |
243 | 6 |
244 | 14 |
245 | 4 |
246 | 1 |
247 | 1 |
248 | 604 |
249 | 1851 |
250 | 3 |
251 | 102978 |
252 | 11 |
253 | 2 |
254 | 2 |
255 | 4 |
256 | 4 |
257 | 1344 |
258 | 2 |
259 | 2 |
260 | 2 |
261 | 5 |
262 | 4 |
263 | 10 |
264 | 5 |
265 | 3 |
266 | 2 |
267 | 1 |
268 | 6 |
269 | 1436 |
270 | 3 |
271 | 12 |
272 | 16680 |
273 | 1 |
274 | 2 |
275 | 980 |
276 | 3 |
277 | 24 |
278 | 2 |
279 | 1 |
280 | 1 |
281 | 2 |
282 | 276 |
283 | 14 |
284 | 36 |
285 | 2 |
286 | 2 |
287 | 4 |
288 | 1 |
289 | 1 |
290 | 24 |
291 | 1 |
292 | 5 |
293 | 44 |
294 | 1 |
295 | 6 |
296 | 4 |
297 | 14313 |
298 | 60670 |
299 | 4 |
300 | 2 |
301 | 2 |
302 | 16 |
303 | 5 |
304 | 70 |
305 | 52 |
306 | 8 |
307 | 203 |
308 | 8 |
309 | 2 |
310 | 1 |
311 | 2 |
312 | 4 |
313 | 4 |
314 | 12 |
315 | 1 |
316 | 5 |
317 | 128 |
318 | 2 |
319 | 564 |
320 | 2 |
321 | 2 |
322 | 17 |
323 | 2 |
324 | 6 |
325 | 2 |
326 | 64756 |
327 | 24 |
328 | 1626 |
329 | 480 |
330 | 1 |
331 | 4 |
332 | 112 |
333 | 1 |
334 | 2 |
335 | 4 |
336 | 2 |
337 | 1 |
338 | 272 |
339 | 10 |
340 | 324 |
341 | 84 |
342 | |
343 | 1 |
344 | 2 |
345 | 1 |
346 | 4 |
347 | 69660 |
348 | 2 |
349 | 1 |
350 | 270 |
351 | 5 |
352 | 1 |
353 | 2 |
354 | 21 |
355 | 2 |
356 | 528 |
357 | 3 |
358 | 1 |
359 | 104 |
360 | 4 |
361 | 6 |
362 | |
363 | 142876 |
364 | 3 |
365 | 2 |
366 | 2 |
367 | 5 |
368 | 36 |
369 | 8 |
370 | 1 |
371 | 22 |
372 | 3 |
373 | 2 |
374 | 52 |
375 | 6 |
376 | 8 |
377 | 16 |
378 | 5 |
379 | 1 |
380 | 2 |
381 | 3 |
382 | 1 |
383 | 4 |
384 | 1 |
385 | 9 |
386 | 2 |
387 | 4 |
388 | 41 |
389 | 70 |
390 | 2 |
391 | 3 |
392 | 4 |
393 | 1 |
394 | 3 |
395 | 2 |
396 | 1 |
397 | 44 |
398 | 56 |
399 | 1 |
400 | 2 |
401 | 16 |
402 | 112 |
403 | 1 |
404 | 2 |
405 | 1 |
406 | 1 |
407 | 500 |
408 | 76 |
409 | 3 |
410 | 42 |
411 | 2 |
412 | 9 |
413 | 4 |
414 | 2 |
415 | 1 |
416 | 180 |
417 | 1 |
418 | 9 |
419 | 4338 |
420 | 10 |
421 | 9 |
422 | |
423 | 2 |
424 | 4 |
425 | 2 |
426 | 3 |
427 | 1 |
428 | 2 |
429 | 6 |
430 | 3 |
431 | 76 |
432 | 99 |
433 | 2 |
434 | 882 |
435 | 1 |
436 | 1 |
437 | 108 |
438 | 126804 |
439 | 15 |
440 | 4 |
441 | 2 |
442 | 16 |
443 | 4 |
444 | 2 |
445 | 3 |
446 | 2 |
447 | 3 |
448 | 1 |
449 | 14 |
450 | 20 |
451 | 2 |
452 | 71940 |
453 | 6 |
454 | 1 |
455 | 1168 |
456 | 1 |
457 | 1 |
458 | 2 |
459 | 3 |
460 | 5 |
461 | 26 |
462 | 80 |
463 | 10 |
464 | 36 |
465 | 2 |
466 | 4 |
467 | 40 |
468 | 18 |
469 | 9 |
470 | 24 |
471 | 263 |
472 | 45 |
473 | 72 |
474 | 2 |
475 | 4 |
476 | 60 |
477 | 1 |
478 | 9 |
479 | |
480 | 15 |
481 | 5 |
482 | 4 |
483 | 2 |
484 | 2 |
485 | 20 |
486 | 4 |
487 | |
488 | 10 |
489 | 2 |
490 | 1 |
491 | 2 |
492 | 27 |
493 | 5 |
494 | 144 |
495 | 2 |
496 | 1 |
497 | 4012 |
498 | 1937 |
499 | 20 |
500 | 2 |
501 | 1 |
502 | 3 |
503 | 892 |
504 | 9 |
505 | 2 |
506 | 2 |
507 | 3 |
508 | 4 |
509 | 194 |
510 | 3 |
511 | 15 |
512 | |
513 | 1 |
514 | 2 |
515 | 6 |
516 | 6 |
517 | 8 |
518 | 2 |
519 | 1 |
520 | 24 |
521 | 8 |
522 | 105 |
523 | 2 |
524 | 814 |
525 | 2 |
526 | 1 |
527 | 328 |
528 | 2 |
529 | 6 |
530 | 4 |
531 | 1 |
532 | 1 |
533 | 6 |
534 | 1 |
535 | 45 |
536 | 9762 |
537 | 56 |
538 | 1 |
539 | 2 |
540 | 12 |
541 | 1 |
542 | 156680 |
543 | 10041 |
544 | 10 |
545 | 1822 |
546 | 131 |
547 | 11 |
548 | 16 |
549 | 23 |
550 | 4 |
551 | 248 |
552 | 1 |
553 | 752 |
554 | 22 |
555 | 1 |
556 | 6 |
557 | 60 |
558 | 32 |
559 | 9 |
560 | 2 |
561 | 1 |
562 | 5 |
563 | 6 |
564 | 38064 |
565 | 2 |
566 | 2 |
567 | 1 |
568 | 1 |
569 | 148 |
570 | 160 |
571 | 10 |
572 | 1832 |
573 | 1 |
574 | 17 |
575 | 34 |
576 | 3 |
577 | 3 |
578 | 2764 |
579 | 2 |
580 | 1 |
581 | 44 |
582 | 4 |
583 | 1 |
584 | 2 |
585 | 1 |
586 | 2 |
587 | 916 |
588 | 106 |
589 | 4 |
590 | 26 |
591 | 10 |
592 | 99 |
593 | 1660 |
594 | 2 |
595 | 11 |
596 | 370 |
597 | 15 |
598 | 4 |
599 | 1018 |
600 | 5 |
601 | 17 |
602 | |
603 | 9 |
604 | 1 |
605 | 6 |
606 | 1 |
607 | 3 |
608 | 2 |
609 | 5 |
610 | 1 |
611 | 274 |
612 | 5 |
613 | 1 |
614 | 30 |
615 | 3 |
616 | 2 |
617 | 16 |
618 | 18 |
619 | 2 |
620 | 972 |
621 | 3 |
622 | 1 |
623 | 2 |
624 | 18 |
625 | 1 |
626 | 8 |
627 | 1 |
628 | 8 |
629 | 2 |
630 | 5 |
631 | 3 |
632 | 4 |
633 | 5 |
634 | 84822 |
635 | 74 |
636 | 1 |
637 | 11 |
638 | 6 |
639 | 3 |
640 | 9 |
641 | 4 |
642 | 3 |
643 | 1 |
644 | 14 |
645 | 1 |
646 | 5 |
647 | 24 |
648 | 6 |
649 | 34 |
650 | 22 |
651 | 131 |
652 | 71 |
653 | 6 |
654 | 2 |
655 | 142 |
656 | 236 |
657 | 4 |
658 | 786 |
659 | 4 |
660 | 3 |
661 | 237 |
662 | 28 |
663 | 2 |
664 | 60 |
665 | 70 |
666 | 2 |
667 | 3 |
668 | 58 |
669 | 1 |
670 | 2 |
671 | 12 |
672 | 1 |
673 | 24 |
674 | 6342 |
675 | 9 |
676 | 3 |
677 | 320 |
678 | 1 |
679 | 2 |
680 | 40 |
681 | 2 |
682 | 616 |
683 | 738 |
684 | 3 |
685 | 6 |
686 | 64 |
687 | 1 |
688 | 172 |
689 | 4 |
690 | 3 |
691 | 314 |
692 | 4 |
693 | 5 |
694 | 227 |
695 | 2 |
696 | 4 |
697 | 1 |
698 | 10 |
699 | 23 |
700 | 23 |
701 | 8662 |
702 | 1 |
703 | 6 |
704 | 12 |
705 | 197 |
706 | 70 |
707 | 12 |
708 | 6 |
709 | 9 |
710 | 2 |
711 | 21 |
712 | 4 |
713 | 14 |
714 | 2 |
715 | 3 |
716 | 8 |
717 | 59 |
718 | 144 |
719 | 16 |
720 | 3 |
721 | 1 |
722 | 972 |
723 | 2 |
724 | 3 |
725 | 4 |
726 | 6 |
727 | 1 |
728 | 16 |
729 | 1 |
730 | 4 |
731 | 14 |
732 | 1803 |
733 | 5 |
734 | 2 |
735 | 3 |
736 | 1 |
737 | 12 |
738 | 86 |
739 | 12 |
740 | 766 |
741 | 4 |
742 | 11 |
743 | 238 |
744 | 1 |
745 | 71 |
746 | 40 |
747 | 20 |
748 | 1 |
749 | 6 |
750 | 2 |
751 | 870 |
752 | 4 |
753 | 40 |
754 | 2 |
755 | 2 |
756 | 1 |
757 | |
758 | 3014 |
759 | 802 |
760 | 267 |
761 | 4 |
762 | 1 |
763 | 1 |
764 | 2 |
765 | 2 |
766 | 81 |
767 | |
768 | 65 |
769 | 1 |
770 | 116 |
771 | 6 |
772 | 3 |
773 | 2 |
774 | 1 |
775 | 3 |
776 | 6 |
777 | 3 |
778 | 4 |
779 | 1014 |
780 | 5 |
781 | 4 |
782 | 1200 |
783 | 1 |
784 | 6 |
785 | 2 |
786 | 1 |
787 | 20 |
788 | 13540 |
789 | 2 |
790 | 5 |
791 | 26 |
792 | 12 |
793 | 1 |
794 | 962 |
795 | 52 |
796 | 9 |
797 | 5188 |
798 | 5 |
799 | 1 |
800 | 12 |
801 | 53 |
802 | 1 |
803 | 2 |
804 | 3 |
805 | 16 |
806 | 2 |
807 | 36 |
808 | 2 |
809 | 10 |
810 | 2440 |
811 | 99 |
812 | 44 |
813 | 1 |
814 | 3 |
815 | 2 |
816 | 6 |
817 | |
818 | 2 |
819 | 1 |
820 | 1 |
821 | 14 |
822 | 3 |
823 | 1089 |
824 | 2 |
825 | 5 |
826 | 1 |
827 | 8452 |
828 | 1 |
829 | 4 |
830 | |
831 | 6 |
832 | 65 |
833 | 18 |
834 | 4 |
835 | 24 |
836 | 1048 |
837 | 1 |
838 | 104 |
839 | 2172 |
840 | 1 |
841 | 12 |
842 | 52 |
843 | 4 |
844 | 9 |
845 | 10 |
846 | 18 |
847 | 1 |
848 | 2 |
849 | 3 |
850 | 5 |
851 | 12 |
852 | 45 |
853 | 2 |
854 | 2 |
855 | 2 |
856 | 1 |
857 | 12 |
858 | 1 |
859 | 2 |
860 | 4 |
861 | 1 |
862 | 11 |
863 | 4 |
864 | 322 |
865 | 1 |
866 | 14 |
867 | 65 |
868 | 5 |
869 | 12288 |
870 | 4 |
871 | 3 |
872 | |
873 | 2 |
874 | 3 |
875 | 58 |
876 | 1 |
877 | 4 |
878 | 114 |
879 | 1 |
880 | 2 |
881 | 2 |
882 | 3 |
883 | 2 |
884 | 2 |
885 | 4 |
886 | 33 |
887 | 32 |
888 | 5 |
889 | 3 |
890 | 37376 |
891 | 1 |
892 | 596 |
893 | |
894 | 11 |
895 | 1 |
896 | 4 |
897 | 27 |
898 | 1 |
899 | 2 |
900 | 1 |
901 | 23 |
902 | 16 |
903 | 302 |
904 | 3 |
905 | 4 |
906 | 4 |
907 | 327 |
908 | 2 |
909 | 3 |
910 | 2 |
911 | 4 |
912 | 1 |
913 | 36 |
914 | 18 |
915 | 3 |
916 | 1 |
917 | 44 |
918 | 653 |
919 | 1 |
920 | 142 |
921 | 1 |
922 | 41 |
923 | 4470 |
924 | 17 |
925 | 2 |
926 | 10 |
927 | 96 |
928 | 1 |
929 | 28 |
930 | 4 |
931 | 3 |
932 | |
933 | 4 |
934 | 51 |
935 | 84 |
936 | 26 |
937 | 56 |
938 | 12 |
939 | 15 |
940 | 42 |
941 | 24 |
942 | 243 |
943 | 5 |
944 | 4 |
945 | 36 |
946 | 2 |
947 | 120 |
948 | 36 |
949 | 9 |
950 | 5956 |
951 | 1 |
952 | 41 |
953 | 60994 |
954 | 2 |
955 | 173 |
956 | 714 |
957 | 17 |
958 | 10 |
959 | 10 |
960 | 1 |
961 | 1 |
962 | 64 |
963 | 81 |
964 | 50 |
965 | 2 |
966 | 6 |
967 | 12 |
968 | 6 |
969 | 2 |
970 | 1 |
971 | 6 |
972 | 15 |
973 | 30 |
974 | 1622 |
975 | 1 |
976 | 3 |
977 | 48 |
978 | 26 |
979 | 4 |
980 | 2 |
981 | 118 |
982 | 1 |
983 | 2 |
984 | 33 |
985 | 3 |
986 | 4 |
987 | 8 |
988 | 1 |
989 | 68 |
990 | 3 |
991 | 1 |
992 | |
993 | 1 |
994 | 1 |
995 | 110 |
996 | 5 |
997 | |
998 | 34 |
999 | 3 |
1000 | 8 |
1001 | 28 |
1002 | 1 |
1003 | 1 |
1004 | 29684 |
1005 | |
1006 | 3 |
1007 | |
1008 | 1 |
1009 | 18 |
1010 | 4 |
1011 | 2 |
1012 | 1 |
1013 | 6 |
1014 | 2 |
1015 | 71 |
1016 | 14 |
1017 | 1 |
1018 | 16 |
1019 | 444 |
1020 | 3 |
1021 | 1 |
1022 | 6064 |
1023 | 1 |
1024 | 38 |
External links
- see Williams prime